Question

There are _________ rational numbers which when multiplied by 0, gives the product as 1.
A. $0$
B. $2$
C. $4$
D. infinite

Answer 1

Hint: To find out how many rational numbers when multiplied by 0 gives a product as 1 we will use some examples. Firstly we will take the first natural number and multiply it by 0 and see the result then accordingly we will conclude how many rational numbers we can get which when multiplied by 0 give the answer as 1.

Complete step-by-step solution:
We have to find the rational number which when multiplied by 0 gives the answer as 1.
So let us take natural number 1 first so,
$1\times 0=0$
We are not getting the answer as 1.
Now let us take another rational number $\dfrac{2}{4}$ so,
$\dfrac{2}{4}\times 0=0$
Again we don’t get the answer as 1.
So we can say that there is no such rational number which when multiplied by 0 gives product as 1 as product of 0 and any number is always 0.
Hence the correct option is (A).

Note: 0 is the most important number in mathematics. It is an integer immediately preceding 1 it is an even number as it is divisible by 2 completely. We can say that 0 is neither positive nor negative or both positive and negative. It may or may not be considered as a natural number but it is an integer and hence it is a rational and real number as well. It can’t be a prime number as it has an infinite number of factors and it can’t be a composite number because we can express it as a product of prime numbers (0 must always be one of the factors).